| It is challenging and important for a firm to make effective decisions under uncertainties, such as random fluctuations of products prices or demands, etc. This dissertation formulates mathematic models to help decision makers in energy and retail industries make optimal timing and optimal operational decisions when facing uncertain electricity prices and demands.;As for energy portfolio management, the optimal entry and dispatch strategies are investigated for an electricity generating firm to introduce a renewable power plant as an alternative method for generating electricity, with or without construction delay. In addition, the abandonment strategies of considering shutting down one of the two power plants in the energy portfolio are studied. To develop these strategies, the expected per unit profit is maximized over a finite time horizon by assuming that the price of electricity follows mean reversion stochastic process. This problem is formulated as a mixed optimal stochastic control and optimal stopping problem. The original problem is solved numerically through two auxiliary problems. Numerical experiments are conducted to confirm the results. The sensitivity analysis of the parameters is conducted to reveal how the uncertainty of electricity price, investment, operation cost, and production rate affect the decisions.;A dynamic inventory model is also developed to study optimal control policy in a finite planning horizon with consideration of debt financing and tax. The model assumes that the retailer raises funds from the financial market and replenishes its stock under the constraint of its cash flow facing random demand. The objective is to maximize the expected terminal wealth. The optimal inventory policy and the optimal debt financing decision with the capital constraint and the effect of tax are obtained. |
